Question

An arrangement of stones that formed an arc of a circle was discovered. If the chord is 12 meters, find the diameter of the completed circle

Answer 1

15 meters

Explanation:

The diagram of the problem is attached below in the first image.

Chords KM and LN (which is the diameter) intersect at X.

Theorem: If the diameter is perpendicular to a chord, it bisects the chord.

Therefore:

LN divides KM into equal parts of 6 meters,

Applying the theorem of intersecting chords:

KX*XM = LX*XN

6*6=3*XN

3*XN=36

XN=12

Next, we find the length of the diameter LN

LN=LX+XN

=3+12

=15 meters

The diameter of the completed circle is 15 meters.